Orientation

One hundred and fifty years ago, one of the most original minds was born: Bertrand Arthur William Russell was a mathematician, logician, philosopher, free thinker... His writings earned him the Nobel Prize in Literature in 1950! His scientific work is colossal. With his accomplice Alfred Whitehead, he gave body to logicism, this school of thought aimed at making the foundations of mathematics rest on logic. His philosophical work is even more considerable. Russell never hesitated to rise against religious, moral or economic dogmas, which he saw as so many shackles from which societies and individuals are prisoners.

The notion of orientation makes it possible to greatly enhance the power and applications of geometry. How to find one's way on a line, on a plane, in space? Why are some objects, like the famous Möbius strip, said to be "non-orientable"? Why do clock hands turn in one direction and not the other? Not all orientation choices are arbitrary and, as is often the case in the history of science, it took several decades to move from intuition to rigor on these questions. If you feel a bit lost, you should find your way through the following pages…